This morning on "Good Morning America," Clinton explained the moment, telling Diane Sawyer she was referring not to what happens to her and Obama individually after the race but what happens to the American people she's met on the campaign trail.

"Running for office, especially nationally, gives you such an intimate look with what's going on in people's lives. It just gets me up and motivates me to try and figure out that I'm going to do to help people who are trying as hard as they can."

Clinton: 'I Don't Make Predictions'

"This race is very close, it's very contested," Clinton said, "I've won some, he's won some. Each of us has to get to 2025 delegates. So of course every single race is important."

Stressing the critical nature of the races, Ohio and Texas among them, Clinton continued when pushed on her husband's comments, "I don't make predictions. I'm just going to wait and see what happens. After all, we have to give the voters a chance to be heard."

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Clinton didn't elaborate, but said she's been having "conversations" with former presidential candidate John Edwards, citing their shared criticism of Obama's health-care plan.

Debate Takes Soft Turn From Showdown

After challenging Obama to weekly debates and ridiculing him in a television advertisement for refusing to debate her, Clinton finally had her chance to go "mano a mano" with Obama in Texas Thursday.

But she did not use the opportunity to strike a game-changing blow. Her final comment of the night — after an hour and 40 minutes of debate — that drew the biggest response.

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Asked to talk about the moment in their lives "that tested you the most," Clinton said: "I think everybody here knows I've lived through some
crises and some challenging moments in my life."

She then said that no matter how bad things have seemed in her life, no matter how tough the challenges, it was nothing compared to what is happening in the lives of Americans every single day.

Clinton reflected on visiting wounded warriors in Texas recently — veterans who arrived in wheelchairs and on gurneys, a speaker who lost part of his face to a roadside bomb.

"You know, the hits I've taken in life are nothing compared to what goes on every single day in the lives of people across our country," she said.

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The call to serve others less fortunate is what "gets me up in the morning," she added. "That's what keeps me going."

And then her voice softened.

"No matter what happens in this contest — and I am honored. I am honored to be here with Barack Obama. I am absolutely honored," she said, and reached across the desk for Obama's hand.

A Tight Battle to Nomination

Given the tight nomination battle she finds herself in, some may read that comment as a poignant admission that she may not end up as the party's nominee.

But just after the debate ended, Clinton's communications director crowed that the final moment was a defining moment for Clinton.

"It was the moment she retook the reins of this race and showed women and men why she is the best choice," said Howard Wolfson.

Obama's team pointed to another part of the debate as his signal moment.

Clinton was criticizing Obama's legislative record.

Obama Surrogate Takes a Hit

"I have to confess, I was somewhat amused the other night, when, on one of the TV shows, one of Sen. Obama's supporters was asked to name one accomplishment of Sen. Obama and he couldn't," Clinton said.

In response, Obama listed some of the legislation he had backed and then hammered his message — referring to the movement his candidacy has spawned.

"I do think there is a fundamental difference between us in terms of how change comes about," he said. "Sen. Clinton of late has said, 'Let's get real.' The implication is that the people who've been voting for me or involved in my campaign are somehow delusional."

"Well, I think they perceive reality of what's going on in Washington very clearly," he added. "What they see is that if we don't bring the country together, stop the endless bickering, actually focus on solutions and reduce the special interests that have dominated Washington, then we will not get anything done. And [that is] the reason that this campaign has done so well."

No All-Out Brawl

If voters came looking for major policy distinctions or an all-out brawl at the University of Texas, they might have left disappointed.

The first 20 minutes of the debate were so civil, it almost seemed like there were no differences between the two candidates' positions.

After one question about a fence along the U.S. border with Mexico — which Clinton said she would look for new technologies and "smart fencing" instead of a physical barrier — Obama responded by saying, "Well, this is an area where Sen. Clinton and I almost entirely agree."

Borrowed Language

"You know, lifting whole passages from someone else's speeches is not change you can believe in, it's change you can Xerox," she said as the audience booed loudly.

She pressed on: "If you look at the YouTube of these videos, it does raise questions."

Immigration Reform Takes Texas Stage

There was a lot of discussion about immigration reform in this heavily Latino state, in a debate co-sponsored by the Univision network.

Perhaps appealing to those Hispanic voters, Clinton for the first time said she would push for comprehensive immigration reform within her first 100 days.

"We need a path to legalization," she said, "to bring the immigrants out of the shadows, give them the conditions that we expect them to meet, paying a fine for coming here illegally, trying to pay back taxes over time, and learning English. If they had a committed a crime in our country or the country they came from, then they should be deported. But for everyone else, there must be a path to legalization. I would introduce that in the first 100 days of my presidency."

Health Care and Foreign Relations

Obama and Clinton discussed their differences on health care at length. And on the prospect of a new leader in Cuba, the candidates differed once again on whether it is appropriate for a president to meet with regimes with whom the United States does not have diplomatic relations.

"Of course the United States stands ready," Clinton said. "And, as president, I would be ready to reach out and work with a new Cuban government, once it demonstrated that it truly was going to change that direction."

"I would not meet with him until there was evidence that change was happening, because I think it's important that they demonstrate clearly that they are committed to change the direction," she clarified.

Obama, on the other hand, was more willing to arrange a meeting with Raul Castro, Fidel's brother who has been acting president in recent months.

"I would meet without preconditions, although Sen. Clinton is right that there has to be preparation," Obama said. "It is very important for us to make sure that there was an agenda, and on that agenda was human rights, releasing of political prisoners, opening up the press. And that preparation might take some time."

"But I do think that it's important for the United States not just to talk to its friends, but also to talk to its enemies," Obama added. "In fact, that's where diplomacy makes the biggest difference."